Abstract
By a Halton–Kronecker sequence we mean a sequence in the (s+t)-dimensional unit-cube which is the combination of an s-dimensional Halton-sequence and a t-dimensional Kronecker sequence. The distribution of such sequences was studied for the first time quite recently by Niederreiter. In this paper we obtain metrical results for the discrepancy of Halton–Kronecker sequences which are similar to results for the pure Kronecker sequences obtained by Khintchine and by W.M. Schmidt.
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R. Hofer was supported by the Austrian Science Fund (FWF), Project P21943 and G. Larcher was supported by the Austrian Science Fund (FWF), Project P21196 and P21943.
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Hofer, R., Larcher, G. Metrical results on the discrepancy of Halton–Kronecker sequences. Math. Z. 271, 1–11 (2012). https://doi.org/10.1007/s00209-011-0848-0
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DOI: https://doi.org/10.1007/s00209-011-0848-0